<PAGE>
 
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                                   FORM 10-Q
                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549
                      __________________________________


(MARK ONE)
 
[X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
     ACT OF 1934

     FOR THE QUARTER ENDED MARCH 31, 1999
 
                                      OR
 
[_]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
     EXCHANGE ACT OF 1934

     For the transition period from _____ TO _____

     Commission file number 1-10877


                         TERRA NITROGEN COMPANY, L.P.
            (Exact name of registrant as specified in its charter)

              DELAWARE                                 73-1389684
  (State or other jurisdiction of          (I.R.S. Employer Identification No.)
  incorporation or organization)


           TERRA CENTRE
  PO BOX 6000, 600 FOURTH STREET
         SIOUX CITY, IOWA                                    51102-6000
  (Address of principal executive office)                    (Zip Code)


                        REGISTRANT'S TELEPHONE NUMBER:
                                (712) 277-1340
                                        
  At the close of business on April 30, 1999, there were 18,501,576 Common Units
  OUTSTANDING.

  INDICATE BY CHECK MARK WHETHER THE REGISTRANT (1) HAS FILED ALL REPORTS
REQUIRED TO BE FILED BY SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE ACT OF
1934 DURING THE PRECEDING 12 MONTHS (OR FOR SUCH SHORTER PERIOD THAT THE
REGISTRANT WAS REQUIRED TO FILE SUCH REPORTS), AND (2) HAS BEEN SUBJECT TO SUCH
FILING REQUIREMENTS FOR THE PAST 90 DAYS.
 X  YES   ___ NO
---            

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<PAGE>
 
                         PART I. FINANCIAL INFORMATION
                                        
                         TERRA NITROGEN COMPANY, L.P.
                          CONSOLIDATED BALANCE SHEETS
                                (in thousands)
                                  (unaudited)


<TABLE>
<CAPTION>
                                                  March 31,  December 31,  March 31,
                                                    1999         1998        1998
                                                  ---------  ------------  ---------
<S>                                               <C>        <C>           <C>
ASSETS
  Current assets:
     Cash and cash equivalents                     $     36      $  1,094   $  1,535
     Accounts receivable                              2,281         6,663      2,389
     Inventory - finished products                   36,489        32,644     31,586
     Inventory - materials and supplies              13,690        17,811     15,287
     Prepaid expenses and other current assets        1,316         2,440      2,961
---------------------------------------------------------------------------------------
  Total current assets                               53,812        60,652     53,758
 
  Net property, plant and equipment                 164,241       164,689    169,073
 
  Other assets                                        8,758        10,736     11,925
--------------------------------------------------------------------------------------- 
 
  Total assets                                     $226,811      $236,077   $234,756
=======================================================================================
 
LIABILITIES AND PARTNERS' CAPITAL
 
  Current liabilities:
      Short-term note payable                      $ 15,197      $    ---   $    ---
     Payable to affiliates                            4,915        23,587        ---
      Accounts payable and accrued liabilities       15,143        18,972     27,043
     Customer prepayments                               737           482      4,306
     Current portion of long-term debt and
      capital lease obligations                       1,132         1,119      1,083
---------------------------------------------------------------------------------------
  Total current liabilities                          37,124        44,160     32,432
 
  Long-term debt and capital lease obligations        7,655         7,846      8,770
  Long-term payable to affiliates                     5,316         5,316      4,996
  Other long-term obligations                           ---           ---      1,060
  Partners' capital                                 176,716       178,755    187,498
---------------------------------------------------------------------------------------
 
  Total liabilities and partners' capital          $226,811      $236,077   $234,756
=======================================================================================
</TABLE>

See accompanying Notes to the Consolidated Financial Statements.

                                                                               2
<PAGE>
 
                         TERRA NITROGEN COMPANY, L.P.
                       CONSOLIDATED STATEMENTS OF INCOME
                    (in thousands, except per unit amounts)
                                  (unaudited)

<TABLE>
<CAPTION>
                                   Three Months Ended
                                       March 31,
                                     1999       1998
                                   ---------  --------
<S>                                <C>        <C> 
Revenues                            $53,784   $48,499
Other income                            289       417
                                    -------   -------
Total revenues                       54,073    48,916
Cost of goods sold                   53,763    40,595
                                    -------   -------
 
Gross profit                            310     8,321
Operating expenses                    2,217     2,443
                                    -------   -------
 
Operating income (loss)              (1,907)    5,878
 
Interest expense                       (432)     (491)
Interest income                         300       414
                                    -------   -------
 
Net income (loss)                   $(2,039)  $ 5,801
                                    =======   =======
 
Net income (loss) allocable to
   limited partners' interest       $(1,997)  $ 5,685
                                    =======   =======
 
Net income (loss) per limited
   partnership unit                 $ (0.11)  $  0.31
                                    =======   =======
</TABLE>

See accompanying Notes to the Consolidated Financial Statements.

                                                                               3
<PAGE>
 
                         TERRA NITROGEN COMPANY, L.P.
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                (in thousands)
                                  (unaudited)

<TABLE>
<CAPTION>
                                                                Three Months Ended
                                                                    March 31, 
                                                                  1999       1998
                                                               ----------  ---------
<S>                                                            <C>         <C>
Operating activities:
 
  Net income (loss)                                             $ (2,039)  $  5,801
  Adjustments to reconcile net income to net cash
    provided by operating activities:
     Depreciation and amortization                                 3,233      3,045
     Changes in operating assets and liabilities:
       Receivables                                                 4,382      1,618
       Inventories                                                   276    (16,195)
       Prepaid expenses                                            1,124       (650)
       Accounts payable, accrued liabilities and
         customer prepayments                                     (3,574)        79
       Payable to affiliate                                      (18,672)       ---
     Change in other assets                                        1,978      4,106
     Other                                                           ---        311
                                                                --------   --------
 
Net cash provided by (used in) operating activities              (13,292)    (1,885)
 
NET CASH USED IN INVESTING ACTIVITIES:
 
  Capital expenditures                                            (2,785)    (2,587)
 
FINANCING ACTIVITIES:
 
  Borrowings of short-term debt                                   15,197        ---
  Repayment of long-term debt and capital lease obligations         (178)      (183)
  Partnership distributions                                          ---    (25,078)
                                                                --------   --------
Net cash provided by (used in) financing activities               15,019    (25,261)
                                                                --------   --------
 
NET INCREASE IN CASH AND CASH EQUIVALENTS                         (1,058)   (29,733)
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                   1,094     31,268
                                                                --------   --------
Cash and cash equivalents at end of period                      $     36   $  1,535
                                                                ========   ========
</TABLE>
See accompanying Notes to the Consolidated Financial Statements.
<PAGE>
 
                         TERRA NITROGEN COMPANY, L.P.

            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1.   Basis of Presentation

     The consolidated financial statements contained herein should be read in
     conjunction with the consolidated financial statements and notes thereto
     contained in the Terra Nitrogen Company, L.P. ("TNCLP") Annual Report on
     Form 10-K for the year ended December 31, 1998. TNCLP and its operating
     partnership subsidiary, Terra Nitrogen, Limited Partnership (the "Operating
     Partnership"), are referred to herein, collectively, as the "Partnership".

     The accompanying unaudited consolidated financial statements reflect all
     adjustments that are, in the opinion of management, necessary for the fair
     statement of the results for the periods presented. All of these
     adjustments are of a normal and recurring nature. Results for the quarter
     are not necessarily indicative of future financial results of the
     Partnership.

     Net income or loss per limited partnership unit is computed by dividing net
     income, less a 2% and 28% share allocable to the General Partner for the
     three months ended March 31, 1999 and 1998, respectively, by 18,501,576
     limited partner units. According to the Agreement of Limited Partnership of
     TNCLP, net loss is allocated to the General Partner and the Limited
     Partners in each period in the same proportion as net income was allocated
     to such Partners in prior years (up to the aggregate of such prior net
     income allocations and beginning with the first taxable year). Net income
     is allocated to the General Partner and the Limited Partners in each
     taxable year in the same proportion as Available Cash for such taxable year
     was distributed to the General Partner and the Limited Partners. If there
     is no cash distribution during a year, net income for that year is
     allocated to the Limited Partners and the General Partner based on their
     respective ownership percentages.

     Distributions of Available Cash are made 98% to the Limited Partners and 2%
     to the General Partner, except that the General Partner is entitled, as an
     incentive, to larger percentage interests (up to 50%) to the extent that
     distributions of Available Cash exceed specified target levels. There was
     no Available Cash for the three months ended March 31, 1999 due primarily
     to the net loss incurred for the period and payment of liabilities.

2.   Distributions to Unitholders

     The Partnership makes quarterly cash distributions to Unitholders and the
     General Partner in an amount equal to 100% of its Available Cash (as this
     and other capitalized terms are defined in the Partnership Agreement). The
     Partnership had no Available Cash, and therefore made no cash
     distributions, for the three months ended March 31, 1999. For the three
     months ended March 31, 1998 the Partnership distributed $21,647,000 (or
     $1.17 per unit) to Common Unitholders and $3,431,000 to the General
     Partner.
 
                                                                               5
<PAGE>
 
3.   Cash and cash equivalents

     The Partnership has demand deposit and demand note arrangements with an
     affiliate to allow for excess Partnership cash to be deposited with or
     funds to be borrowed from Terra Capital, Inc., the parent of the General
     Partner. The balance is due on demand and at March 31, 1999 the interest
     rate was 7.45%. The amount owed by the Partnership under the demand note
     was $15.2 million at March 31, 1999.

4.   Natural gas costs

     The Partnership's natural gas procurement policy is to effectively fix or
     cap the price of between 40% and 80% of its natural gas requirements for a
     one-year period and up to 50% of its natural gas requirements for the
     subsequent two-year period through supply contracts, financial derivatives
     and other forward pricing techniques. These contracts reference physical
     natural gas prices or appropriate NYMEX futures contract prices. Contract
     physical prices are frequently based on the Henry Hub Louisiana price, but
     natural gas supplies for the Partnership's production facilities are
     physically purchased from various suppliers which often creates a location
     basis differential between the contract price and the physical price of
     natural gas. Accordingly, the use of financial derivatives may not exactly
     offset the change in the price of physical gas. The contracts are traded in
     months forward and settlement dates are scheduled to coincide with gas
     purchases during that future period.

     The Partnership has entered into firm contracts to minimize the risk of
     interruption or curtailment of natural gas supplies. Additionally, the
     Partnership has entered into forward pricing positions for a substantial
     portion of its natural gas requirements for the remainder of 1999 and 2000,
     consistent with its policy. As a result of its policies, the Partnership
     has reduced the potential adverse financial impact of natural gas price
     increases during the forward pricing period, but conversely, if natural gas
     prices were to fall, the Partnership will incur higher costs. Unrealized
     gains from forward pricing positions totaled $1.6 million and $24.8 million
     as of March 31, 1999 and 1998, respectively. The amount recognized by the
     Partnership will be dependent on prices in effect at the time of
     settlement.

     For the first three months of 1999 and 1998, natural gas hedging activities
     resulted in additional costs of approximately $5.1 million and cost savings
     of $1.8 million, respectively, compared with spot prices.

                                                                               6
<PAGE>
 
        MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
                             Results Of Operations
                                        
                             RESULTS OF OPERATIONS
                                        
               Three months ended March 31, 1999, compared with
                       Three Months Ended March 31, 1998
                                        

Volumes and prices for the three-month periods ended March 31, 1999 and 1998
were as follows:

<TABLE>
<CAPTION>
                                      1999                                       1998
                         ----------------------------           -----------------------------------
                              Sales          Average                 Sales               Average
                             Volumes        Unit Price              Volumes             Unit Price
                           (000 tons)        ($/ton)               (000 tons)            ($/ton)
                         ------------     -----------           -------------       ---------------
<S>                      <C>              <C>                   <C>                 <C>
Ammonia                       131              104                    63                    142     
UAN                           470               61                   390                     63     
Urea                          127               91                   137                    108     
</TABLE>

Revenues for the quarter ended March 31, 1999 increased $5.2 million, or 11%,
compared with the same quarter in 1998 due to significantly increased volumes of
ammonia and UAN products. Decreased volumes of urea sales as well as lower
average unit prices for all of the Partnerships products offset the effects on
revenue for most of these volume increases. Surplus worldwide nitrogen
production continued to put pressure on prices during the 1999 quarter resulting
in price reductions of 27%, 3% and 16% for ammonia, UAN and urea, respectively,
compared with the 1998 quarter.    Volumes were more than the comparable quarter
a year ago due to customers' decisions to delay late 1998 purchases to fill
storage in anticipation of continuing price reductions, and an early start to
the planting season due to favorable weather conditions in the southeast.

Cost of goods sold as a percentage of revenues increased to 99% for the 1999
quarter from 83% in the 1998 period primarily due to the lower nitrogen selling
prices. Gas costs increased 4% during the 1999 quarter compared with the 1998
quarter.  The Partnership's natural gas forward pricing activities produced $5.1
million in additional costs during the 1999 period.

Operating expenses decreased $0.2 million, or 9%, due to lower pension,
administrative, and overhead expense allocations from Terra Nitrogen Corporation
and Terra Industries.

Net interest increased slightly compared with the 1998 period primarily due to
the loss incurred for the period.

                                                                               7
<PAGE>
 
CAPITAL RESOURCES AND LIQUIDITY

Net cash used in operating activities for the first three months of 1999 was
$13.3 million to fund the loss for the period and repay affiliates for trade
items.  These uses were partly offset by reductions to accounts receivable,
prepaid expenses and other assets.

The Partnership's principal needs for funds are for support of its working
capital, distributions to Partners, and capital expenditures. The Partnership
intends to fund such needs primarily from net cash provided by operating
activities and, to the extent permitted thereunder, from funds available under
the Operating Partnership's revolving credit facility.  Under certain
circumstances an affiliate of the Partnership may advance funds to the
Partnership under a demand note.  At March 31, 1999, the Operating Partnership
had $18 million of unused borrowing capacity under its revolving credit
facility, and had $15.2 million outstanding under a demand note with an
affiliate.  The Partnership believes that such sources of funds will be adequate
to meet the Partnership's working capital needs, make quarterly distributions to
Partners and fund the Partnership's capital expenditures for at least the next
twelve months.

On April 22, 1999, Terra Nitrogen Company, L.P. announced there would be no cash
distribution for the quarter ended March 31, 1999 since there was no Available
Cash for distribution for the quarter.

                             CAPITAL EXPENDITURES
                                        
Capital expenditures totaled $2.8 million for the first three months of 1999.
For the remainder of 1999, the Partnership plans to spend approximately $4.1
million.  Plans for 1999 include the purchase of heavy equipment to be installed
in 2001 at the Blytheville plant and environmental control, equipment
replacement and efficiency and capacity improvements at both plants.


                                YEAR 2000 ISSUE
                                        
The Year 2000 issue concerns computer programs that use only the last two digits
to identify the year in date fields. If not corrected, many of these computer
applications could fail or create erroneous results near January 1, 2000. This
issue affects virtually every company.

The Partnership relies upon Terra to provide Management Information Systems
services.

Terra has assigned dedicated resources to address its year 2000 issues with a
Year 2000 Steering Committee providing management oversight and coordination.
The Partnership has also published Year 2000 Information and Disclosures on
Terra's website (http://www.terraindustries.com). In general, management
                 -------------------------------                        
believes the "State of Readiness" for the Partnership is such that it will be
ready for Year 2000 issues on time.

Terra's management information systems (MIS) environment has been assessed for
Year 2000 issues and some remedial actions have been identified. The cost of
remedial actions for the MIS area is not material to the Partnership. Nearly all
of these remedial actions are complete with minimal cost. Testing is
substantially complete with the mainframe hardware systems and the associated
software, 

                                                                               8
<PAGE>
 
with the exception of a few software packages originally purchased from third
parties that are scheduled to be updated in 1999.

Organization-wide reviews of all possible computing functions have been
completed, including the process control systems and instrumentation in the
manufacturing facilities. Some remedial actions have been identified in a few
areas and the cost of these remedial actions is not expected to be material to
the Partnership.

Terra is also assessing Year 2000 issues in relation to its customers, suppliers
and other constituents because the action or inaction of third parties may
materially affect the Partnership. An initial assessment of key third parties,
including utility suppliers, has been completed and some follow up is ongoing.

Although the Partnership expects that there will be no significant adverse
consequences relating to its Year 2000 issues, the Partnership believes its most
reasonably likely worst case Year 2000 scenario involves the interruption of its
manufacturing facilities due to failed utility supplies or some other cause. The
Partnership has in place contingency plans to deal with such interruptions,
although restarting these facilities may be dependent on the resumption of
utilities from sole source suppliers. Other general contingency planning efforts
continue to be evaluated and refined for precautionary purposes.

Terra anticipates that it will complete all assessment, remediation, testing,
and contingency planning efforts for Year 2000 issues in the third quarter of
1999. Based on substantial completion of activities to date, the Partnership
anticipates that Year 2000 issues, including the historical and estimated costs
of remediation, will not have a material effect on its business, results of
operations or financial condition. However, the costs or consequences of
incomplete or untimely resolution of Year 2000 issues by the Partnership or
third parties could have a material adverse affect on the Partnership.


                              LIMITED CALL RIGHT
                                        
If at any time not more than 25% of the Common Units are held by non-affiliates
of the General Partner, either TNCLP, the General Partner or its affiliates may
call all such outstanding units held by non-affiliated persons in accordance
with the terms of the TNCLP partnership agreement.  TNCLP is required to give at
least 30 but not more than 60 days notice of its decision to purchase the
outstanding Common Units.  The purchase price per unit is required to be the
greater of (1) the average of the previous twenty trading days closing prices as
of the date five days before the purchase is announced or (2) the highest price
paid by the General Partner or any of its affiliates for any unit within 90 days
preceding the date the purchase is announced.

The General Partner and its affiliates own 69% of the Common Units as of March
31, 1999.  Under existing authorization of the board of directors of Terra
Industries, Inc., the indirect parent of the General Partner, additional Common
Units may be purchased on the open market and through privately negotiated
transactions by affiliates of the General Partner to bring this ownership level
above 75%.  Although TNCLP and its affiliates reserve the right to consider in
the future whether to acquire all of the Common Units, they do not have any
present plan or intention to do so.

                                                                               9
<PAGE>
 
                          FORWARD LOOKING PRECAUTIONS
                          ---------------------------

Information contained in this report, other than historical information, may be
considered forward looking.  Forward looking information reflects Management's
current views of future events and financial performance that involve a number
of risks and uncertainties.  The factors that could cause actual results to
differ materially include, but are not limited to the following: general
economic conditions within the agricultural industry, competitive factors and
price changes (principally, sales prices of products and natural gas costs),
changes in product mix, changes in the seasonality of demand patterns, changes
in weather conditions, changes in agricultural regulations, and other risks
detailed in the Partnership's Securities and Exchange Commission filings, in
particular the "Factors that Affect Operating Results" section of its most
recent Form 10-K.

                          PART II.  OTHER INFORMATION

ITEM 5.  OTHER MATTERS

      The majority shareholder of Terra Industries Inc. has announced its
      intention to sell its stake in Terra Industries.  Terra Industries is the
      indirect parent of the General Partner and the indirect majority owner of
      approximately 70% of Terra Nitrogen Company, L.P.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

      (a)  Exhibits:

     10.40 Limited Waiver dated as of March 22, 1999 to the 1998 Credit
           Agreement, filed as Exhibit 4.5 to the Terra Industries Inc. Form 10-
           Q for the quarter ended March 31, 1999 (File No. 1-8520), is
           incorporated herein by reference.

       27  Financial Data Schedule. (EDGAR  only)

       (b) Reports on Form 8-K:
 
       None.

                                                                              10
<PAGE>
 
                                   SIGNATURE

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                          TERRA NITROGEN COMPANY, L.P.

                                     By:  TERRA NITROGEN CORPORATION
                                          as General Partner


                                     By:  /s/ Francis G. Meyer
                                          ------------------------------------
                                          Vice President 
                                          (Principal Accounting Officer)



Date:  May 14, 1999

                                                                              11